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The present work focuses on the modelling of the fatigue behaviour of a 316L produced by laser powder bed fusion containing various defect populations : Lacks of fusion, corrosion pits and one electric discharge machined hemispherical defect. As shown in previous experimental studies, the crack leading up to failure systematically initiated on a single surface defect. The nature and morphology of the critical defect did not show any influence on the fatigue strength, and only its size seemed to matter. To take into account the critical defect size, models based on linear elastic fracture mechanics were implemented and identified. A modified Paris propagation law was used to model the short crack regime. This approach was used to predict S–N curve domains based on critical defects size range. PhD grant from the French region Pays de la Loire

International audience; The mechanical performances of additive manufactured (AM) material are highly dependent on the fabrication process which inevitably results in surface imperfection as well as porosity. In the present study, the high cycle fatigue (HCF) behavior of an AM stainless steel 316L is experimentally investigated to characterize and evaluate the effect of the inherent surface defects. Profilometry and Computed Tomography are used. A series of fatigue experiments is carried out under different loading modes including tension, bending, and torsion fatigue tests. For each loading condition, different surface preparations are used to investigate the effect of surface state. Fatigue tests reveal that surface treatment can improve fatigue performances, the improvements observed being higher under tension/bending loading than under torsion loading. The fractographic analysis is performed for all the available tested specimens to reveal the mechanism of fatigue crack initiation. Lack-of-fusion (LoF) defects play the predominant role in the fatigue performance of SS 316L fabricated by laser powder bed fusion (LPBF). The presence of multiple LoF defects at the surface or subsurface is detrimental to the endurance under cyclic loading. By using Murakami approach modeling the relationship between fatigue strength and defect size, it is found that the multiple clustering defects act synergistically as one large virtual crack to initiate the fatigue crack.

International audience; In this work, stainless steel 316L obtained by Laser Powder Bed Fusion (L-PBF) has been produced and characterized. The experimental campaign focuses on the samples in the as-built state under cyclic tension-compression loadings. Low cycle fatigue (LCF) and high cycle fatigue (HCF) tests are carried out. Microstructure observations are performed before and after the loadings. As-built L-PBF 316L has a good LCF performance despite the presence of surface defects but a low fatigue limit in the HCF regime. Removing the surface roughness has a beneficial effect but does not improve the fatigue strength to that of machined wrought 316L. Observations on the microstructure of fatigue samples indicate that LCF is dominated by the local plastic deformation, which is mostly achieved by the slip in the studied material and is not sensitive to the defect. The lack-of-fusion defect impairs the fatigue resistance in the HCF regime.

Two cast aluminium alloys fabricated by different casting processes (gravity die-casting and lost foam casting) and showing different degrees of porosity were characterized with X-ray Computed tomography. Information concerning the pore distribution inside the investigated materials is obtained in terms of pore size and the pore positions in 3D space. Subsequently, a spatial point pattern analysis is undertaken to investigate the pore distributions. Different methods, including a nearest neighbor analysis, Ripley's K-function and Clark-Evans tests developed for 3D applications, are used to analyse the observed patterns. The results show that the Homogeneous Poisson process, which provides the Complete Spatial Randomness (CSR) is suitable to approximate the spatial distribution of the pores present in the investigated alloys. Synthetic microstructures that mimic key macroscale features of the materials in terms of pore size and the 3D spatial distribution of the pores were generated. These microstructures can be used in the probabilistic modelling of fatigue behavior.

International audience; This paper aims to study the individual and competitive effects of surface defects and microstructural compo­nents in an AM 316L by numerical methods. Based on the microstructure sensitive modeling framework, nu­merical simulations of models in different surface states with virtual quasi-realistic explicit microstructures are performed. Problems encountered during the establishment of the numerical polycrystalline aggregate model are discussed, including the grain morphology, the strongly textured microstructure with preferential crystallo­graphic directions, roughness and surface defect. A statistical method based on generalized extreme value dis­tribution along with a non-local method is used to describe the stochasticity of microstructural attributes. Simulations of differently configured explicit microstructure models are analyzed and discussed.

In this study, a probabilistic model based on Monte-Carlo theory is applied to predict the fatigue behavior of cast aluminum alloys. The objective of the proposed approach is to investigate the effect of porosity (i.e. the defect size distribution and spatial density) on the fatigue strength and its associated scatter for uniaxial fatigue loads with the load ratio R = 0.1. The proposed model is applied to two cast aluminum alloys with very different defect characteristics. The results for these two alloys confirm that the model can be used to predict the average fatigue strength with a relative error

Corrosive environments are known to be detrimental to the mechanical strength of metallic alloys. In the case of 316L stainless steel, the main corrosion mechanism observed is pitting, which leads to localized rough defects. As for other materials submitted to cyclic loadings and prone to pit, corrosion defects tend to be at the core of crack initiation leading to failure. The work here-by presented will thus focus on the relationship between the fatigue performance and the presence of process or corrosion related defects for a 316L stainless steel manufactured by Laser Powder Bed Fusion (L-PBF). To do so, cylindrical samples were produced vertically, then machined to fatigue specimens in as-built state (no heat treatment). Specimens were polished in order to only characterize the bulk material and not its raw surface. The fatigue responses of three batches corresponding to three configurations of surface integrity (polished, pre-corroded and with an Electric Discharge Machined (EDM) defect) were investigated. For the polished batch, fracture surface observations showed that initiation started from a lack of fusion (LoF) surface pore in all specimens. The pre-corroded batch was prepared under potentiodynamic anodic polarization conditions in a neutral NaCl solution. On those samples, some cracks initiated on corrosion pits, depending on the severity of the corrosion applied to each sample and its initial population of defects. For the EDM batch, a hemispherical defect, at the source of all failures, was machined in the middle of the gauge length. A good correlation between Murakami’s square root of the area parameter and the fatigue strength was observed on a Kitagawa-Takahashi diagram for all tested specimens. This correlation showed an independence of the defect type (LoF, pit, machined defect) on the specimens fatigue strength. Defect morphology doesn’t seem to be an important driving force for crack initiation as ellipsoidal corrosion pits, hemispherical EDM defects and flat lacks of fusion, although very different in terms of shape, are just as harmful at equivalent sizes. This research was funded by a PhD grant from the French region Pays de la Loire.

International audience; Cast Al-Si alloys have been widely used in automotive applications with regard to their low density and excellent thermal conductivity. Many components made of these alloys are subjected to cyclic loads which can lead to fatigue failure. Furthermore, for these materials the well know size effect in fatigue, whereby the fatigue strength is reduced when the size is increased, can be significant and need to be properly evaluated. This paper analyses the role of casting defects on the fatigue strength’s size effect sensitivity. A uniaxial fatigue testing campaign (R=0.1) has been conducted using two cast aluminium alloys, fabricated by different casting processes (gravity die casting and lost foam casting), associated with the T7 heat treatment, and with different degrees of porosity. The fatigue response of different specimens (smooth and notched) with different stressed volumes has been investigated. The first part of this article is dedicated to the experimental characterization of the size effect in both alloys via the concept of the Highly Stressed Volume. The second part investigates the effect of the Highly Stressed Volume on the critical defect size via Kitagawa-Takahashi diagrams. The results show that the magnitude of the size effect and the experimental scatter are strongly linked to the characteristics of the defect population present in the alloy. It is revealed that the alloy B, with a high density of pore and a population of defects with relatively large size, shows non-significant size effect and less scatter in fatigue strength. In comparison, alloy A that exhibits a low density of pore and a population of defects of relatively small size manifests significant size effect and high scatter in fatigue strength.

This work is focused on the influence of porosity when dealing with the fatigue behaviour of TA6V alloys fabricated by the selective laser melting (SLM) process. The presence of porosity is one of the major issues facing additive manufacturing (AM) of metallic components subjected to fatigue loading. In order to study the effect of porosity on the fatigue behaviour, a vast experimental campaign has been undertaken. Seven specimen batches, fabricated by the SLM process with different building directions (horizontal, vertical and diagonal) were tested and a large amount of data was obtained. The link between the applied stress, the fatigue life and the pore size is highlighted by using generalized Kitagawa-Takahashi maps. It is shown that the effect of porosity on the fatigue strength is much more pronounced compared to the effect of the microstructure. In the modelling section, two approaches based on fracture mechanics are considered. The first one is based on the Paris law which is used to model long fatigue crack growth. The second approach was proposed by Caton et al. (2001) for modelling small fatigue crack growth. Finally, a simulation of the generalized Kitagawa-Takahashi is presented and good agreement with the experimental data is shown. This study is part of the FATAL project, managed by IRT Jules Verne (French Institute in Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures). The authors wish to associate the industrial and academic partners of this project; Respectively ACB, Arts et Métiers ParisTech, CNRS, DAHER, Ecole Centrale de Nantes, Europe Technologies, FIVES, Renault and University of Nantes.

This article describes a microstructural-based high cycle fatigue strength modelling approach applied to different cast Al-Si alloys used in an automotive context. Thank to different casting processes (gravity die casting and lost foam casting), associated with several heat treatment (T7 and Hot Isostatic Pressing-HIP), three alloys with very different microstructures have been obtained. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms governing these alloys under different multiaxial loading conditions, it was shown that the principal crack initiation mechanisms for the porosity-free alloy are either the formation of persistent slip bands (PSB) or the rupture and/or debonding of eutectic particles. For the porosity-containing alloys, the fatigue damage is always controlled by crack growth from pores. In order to take into account these fatigue damage mechanisms, a probabilistic model using a combination of the Dang Van and a modified LEFM criteria is proposed. The modified LEFM criterion is able to take into account the influence of the grain size on the threshold of the stress intensity factor. It is shown that for the porosity-free alloy, the predictions are good for combined tension-torsion loads with R = - 1 . However, because the crack initiation mechanisms are not the same depending on the hydrostatic stress, the predictions are non-conservative for the uniaxial and equibiaxial tension loads with R = 0.1 . For the porosity-containing alloys, the predictions are very good for the uniaxial, combined tension-torsion and equibiaxial tension loads with both R = - 1 and R = 0.1 . As observed experimentally, the proposed model can also predict a more pronounced effect of casting porosity for the uniaxial and combined tension-torsion loads, when compared to pure torsion loads.

International audience; This work is focused on the influence of defects on scatter and statistical size effect of Ti-6Al-4V alloy fabricated by the SLM process. A vast fatigue test campaign has been undertaken, for two surface conditions (as-built and machined surfaces) and two specimen geometries with different highly loaded volume sizes. It was shown, for machined specimens, that a large variety of crack initiation mechanisms is the principal origin of the fatigue scatter. Regarding the size effect, the change of the mechanism is the first order factor that governs the size effect. For as-built specimens, these effects are much less pronounced.

International audience; This study aims at investigating the effect of defect on the high cycle fatigue behavior of polycrystalline aggregates. An explicit virtual microstructure finite element model is created to conduct fatigue simulations. Different stress-based criteria frequently applied in fatigue assessment are tested with a combination of the non-local methods. Two realizations of the non-local method are used and compared. Simulation results are compared to experimental results of 316L. From the parametric simulations, better qualitative understandings on the choice of non-local method as well as its parameters are obtained. The effect of Kitagawa-Takahashi can be reproduced and explained by this proposed framework of microstructure modeling-simulation.

International audience; The aim of this study is to understand the impact of periodic surface micro-geometry patterns (obtained by High Speed Machining process) on the fatigue behavior of the AA7050 aluminium alloy and to define a proper defect acceptability criterion. It must be able to account for a large range of surface defects and of component sizes and geometries (wings, brackets, frames, etc.). A vast experimental campaign under fully reversed plane bending loads containing different surface states has been undertaken to characterize the effect of the surface topography on the fatigue behavior. The results show that the fatigue strength decreases when the surface roughness is significantly degraded. In order to predict the influence of the surface condition on the fatigue behavior, a numerical approach based on the real surface topology has been developed. It is shown that the numerically identified crack initiation sites are in agreement with the experimental results. A probabilistic approach based on the weakest link concept, associated with the definition of a stress based crack initiation threshold has beenintegrated in a FE model. This approach leads to a probabilistic diagram inspired from the Kitagawa type diagram, which explains the relationship between the surface and the scale effect on the fatigue strength.

International audience; Polycrystalline elasto-plasticity models provide a general framework for investigating the effect of microstructural heterogeneities (e.g. grains, inclusions, pores) on the high cycle fatigue behavior of metallic materials. In this work, continuum damage mechanics is used to construct a set of constitutive relations to describe the progressive degradation of certain mechanical properties at the grain scale. The damage is considered to be coupled with the elastic behavior of the material. Special care is taken to include the anisotropic aspect of fatigue damage and the effect of intragranular internal stresses. The constitutive relations are then implemented within a self-consistent model to evaluate intergranular interactions. Finally, the model is used to investigate the high cycle fatigue behavior of polycrystalline copper. It is shown that the influence of certain loading conditions on the high cycle behavior is correctly reproduced. Specifically, the application of a mean shear stress does not result in an increase in damage; however, a mean normal stress is damaging. That is, a decrease in the fatigue resistance is predicted when the mean normal stress is increased.

International audience; Geometrical defects are known to have a detrimental influence on the high cycle fatigue resistance of metallic alloys, smaller defects being less harmful. In this experimental work, the influence of the defect size on the high cycle fatigue behavior of polycrystalline aluminium with different grain sizes is investigated, to better understand the role of internal length scales. Firstly, different thermomechanical treatments are applied to obtain aluminium samples with either small (100 μm) or large (1000 μm) grains. The samples are used for preparing fatigue specimens, with either small (100 μm) or large (1000 μm) hemispherical defects. Fully reversed stress-controlled fatigue tests are then carried out. According to fatigue test results, surface crack initiation is delayed when the grain size is reduced, while an approximation of the fatigue limit shows that it is not much influenced by the average grain size. The influence of grain size seems to be explained by the role of cyclic plasticity in the crack initiation process. Finally, Electron BackScattered Diffraction (EBSD) maps are collected for specimens with large grains and small defects. Based on this experimental dataset, fatigue crack initiation from a defect is found to be strongly impacted by the crystallographic orientation of the surrounding grain, crack initiation preferably occurring in crystals being favorably oriented for plastic slip.

Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.

In the present study, the effects of both the microstructure and voids on the high-cycle fatigue behaviour of the 316L austenitic stainless steel are investigated by using finite element simulations of polycrystalline aggregates. The numerical analysis relies on a metallurgical and mechanical characterization. In particular, fatigue tests are carried out to estimate the fatigue limits at 2.106 cycles under uniaxial and multiaxial loading conditions (combined tension and torsion and biaxial tension) using both smooth specimens and specimens containing an artificial hemispherical defect. The simulations are carried out with several configurations of crystalline orientations in order to take into account the variability of the microstructure in the predictions of the macroscopic fatigue limits. These predictions are obtained, thanks to a probabilistic fatigue criterion using the finite element results. The capability of this criterion to predict the influence of voids on the average and the scatter of macroscopic fatigue limits is evaluated.

International audience; This study aims to examine the effects of both material microstructure and voids on the high-cycle fatigue behavior of metals. To deal with this matter, finite element analyses of polycrystalline aggregates are carried out, for different configurations of crystalline orientations, in order to estimate the mechanical state, at the grain scale, in the vicinity of a small elliptical hole. Fatigue criteria are then applied to estimate the average fatigue limit in fully reversed tension, for different defect sizes and ellipse aspect ratios.The constitutive models and the fatigue criteria are calibrated using experimental data obtained from specimens made of 316L austenitic steel. The estimations are then compared with the experimental trends.

International audience; The aim of this paper is to propose a flexible multiaxial modelling framework that is capable of combining two fatigue damage mechanisms so as to continuously describe the Kitagawa-Takahashi diagram. It is proposed that this diagram represents two distinct fatigue damage mechanisms: one associated with crack initiation (or microstructurally small cracks) and the other with crack propagation (or long cracks). It is further postulated that these damage mechanisms are more appropriately modelled using di erent fatigue criteria. A probabilistic modelling framework is proposed in which any two suitable fatigue criteria can be combined in order to simultaneously model both damage mechanisms and the transition between them. This framework is based on the weakest link hypothesis and results in a probabilistic Kitagawa-Takahashi type diagram.

Lien vers la version éditeur: http://www.sciencedirect.com/science/article/pii/S0167663613000288; International audience; To obtain robust estimations of the fatigue limit from energy-based fatigue criteria, constitutive laws must include a correct description of the energy balance when modeling the cyclic behavior. The present paper aims at providing a better understanding of the evolution of the energy balance at both microscopic and macroscopic scales in a medium carbon steel. First, an experimental procedure is used to estimate the amount of energy which is either stored in the material or dissipated into heat at a macroscopic scale. The energy balance is observed to be very dependent on the stress amplitude and the number of loading cycles. A model is then developed to investigate the energy balance at a microscopic scale. From the simulation results, both the stored energy and dissipated energy fields are found to be strongly scattered. The dispersion is mostly explained by the crystallographic orientation distribution and the two-phased microstructure.

Hot-forging is a process commonly used in the manufacturing of automobile parts such as connecting rods. Most hot-forged components are shot-blasted after forging in order to clean off the forging scale. The shotblasting process is akin to shot-peening and greatly affects the surface integrity of the components by introducing hardening and residual stresses. This study focuses on the influence of the surface integrity on the fatigue behaviour of a hot-forged C70 steel connecting rod. Specimens were machined out of the connecting rods in order to perform fatigue testing on the forged surface. Several surfaces states, including shot-peened surfaces, were studied in order to quantify the influence of the surface integrity. A thorough characterisation of the surface integrity of the specimens was first performed. The hardness, residual stresses and microstructure gradients were analysed, and the surface of each specimen was scanned using a profilometer. The specimens show complex networks of surface defects introduced during forging, and the shot-blasting process introduces important surface residual stress and microstructure gradients. High cycle fatigue tests in plane bending were then performed on the specimens, with the surface scans helping to identify the critical defect on which crack initiation occurred. The fatigue results, presented in the form of a Kitagawa diagram, are analysed in order to determine which surface integrity parameters are the most influential on fatigue behaviour. The forging defects have an important negative effect on fatigue strength. After shot-blasting, the fatigue strength increases considerably because of the large compressive residual stresses introduced by the shot-blasting process. This work has been performed within the ANR (National Research Agency) DEFISURF project, in a partnership including several industrial (Ascometal, CETIM, Renault, Transvalor, Atelier des Janves, Gévelot Extrusion) and academic (INSA Lyon MATEIS, ENSMPCEMEF, Arts et Métiers ParisTech LAMPA) institutions.

International audience; This article presents a review of selected multiaxial high-cycle fatigue criteria with an emphasis on their ability to take into account the mean stress effect and the effect of a biaxial stress state. It is shown that the predictions of the various criteria are very different for the case of biaxial tensile loads. This is in contrast to the case of combined tension-torsion loads, where the predictions are very similar. The second part of the article investigates which mechanical parameter (eg, the hydrostatic stress or the normal stress) is the most appropriate to take into account these cyclic stress states.

In this study, various experimental methods are employed to determine the anisotropic fatigue behavior of a 25MnCrSiVB6 forged steel (Metasco MC). This material has a bainitic microstructure and contains many elongated non-metallic inclusions in the rolled direction, which are grouped into clusters. Specimens with different orientations relative to the rolling direction have been extracted from a hot rolled bar and the ability of certain experimental techniques to capture the fatigue anisotropy has been tested. Results obtained from monotonic tensile tests and Charpy impact tests show that the material has isotropic fracture strength and anisotropic ductility. The influence of the inclusion clusters is clearly demonstrated via observation of the fracture surfaces. Concerning the fatigue behavior, results from a classical staircase experimental procedure are compared to results from self-heating fatigue tests. For specimens orientated at 0° relative to the rolled direction, microcrack initiation is controlled by the material matrix and the prediction of the fatigue strength with the self-heating method has been observed to be correct. For specimens orientated at 45° and 90°, the elongated manganese sulfide inclusion clusters are the origin of crack initiation and the fatigue strength drops significantly. For this case, it appears that the self-heating method has difficulty predicting the fatigue behavior.

The authors gratefully acknowledge the financial support of PSA – Peugeot Citroen and also that of the Conseil General du Departement de Maine-et-Loire, France.

The work proposed in this paper is a possible way of modelling some local observations at the surface of mild steel specimens submitted to uniaxial and multiaxial loads. It is clearly seen that local plasticity, controlled by local microstructural heterogeneities, plays a fundamental role in microcrack nucleation and damage orientation is closely related to the applied loading mode. The framework of irreversible thermodynamics with internal variables for time-independent, isothermal and small deformations has been used to build a critical plane damage model by assuming the existence of a link between mesoplasticity and mesodamage. Non-associated plasticity and damage rules allow the evolution of some plastic slip before any damage nucleation, as seen during the observations. A key feature of this proposal is the capacity to reflect nonlinear damage accumulation under variable amplitude loading.

In this paper, a polycrystalline model is proposed to describe the fatigue behaviour of metallic materials in the high cycle fatigue regime. The model is based on a multiscale approach, which allows the connection of local deformation and damage mechanisms to macroscopic behaviour. To consider the anisotropy of plastic properties, the constitutive model is developed at the grain scale within a crystal plasticity framework. A phenomenological approach, which requires the introduction of a damage variable for each slip system, is used to account for the anisotropic nature of damage. The constitutive model is then integrated within a self-consistent formulation to consider the polycrystalline nature of metallic materials. Finally, the proposed model is used to describe the high cycle fatigue behaviour of a medium carbon steel (0.35% C). With a proper adjustment of material parameters, the model is capable of correctly reproducing fatigue test results, even for complex loading conditions (multiaxial, non-proportional). According to the model, damage is found to be highly localized in some specific grains. Also, while fatigue damage results in a progressive decrease in elastic stiffness at the crystal scale, the elastic properties are not significantly affected at the macroscopic scale. The model is used to study the correlation between energy dissipation and fatigue damage. According to the numerical results, no evident correlation between fatigue damage and energy dissipation is observed.

Cold extrusion is a process commonly used to manufacture drive train components in the automotive industry. Large plastic strains can be applied during this operation (up to 1.5) and greatly changes the mechanical properties of the resulting material. This study focuses on the impact of cold extrusion process parameters on the multiaxial fatigue behaviour of steel components. A specific set of forward rod extrusion tools was developed to get original fatigue specimen able to characterise the effect of the manufacturing process on the fatigue behaviour. The specimens were extruded from two different initial diameters, giving two different reductions in cross-section of 18% and 75% respectively. To understand the influence of cold extrusion, the following analyses have been undertaken for each condition and on the initial material: monotonic tensile properties, microstructure, EBSD, residual stresses and hardness. Simulation of the forming process and microstructural observations show that the plastic strain is homogeneous in the specimen section. For both reduction factors, the forming process has a positive effect on the components properties: induced residual stresses in compression and improved hardness and roughness (Ra decreasing). Tension, plane bending and torsion fatigue tests show that the fatigue strength is about 30% higher for the batch with 75% reduced cross-section. All investigations show that strain hardening is the principal material parameter responsible for the increase in fatigue strength. A multiaxial fatigue criterion taking into account the effects of the forward rod extrusion process was also developed. This work has been performed within the ANR (National Research Agency) DEFISURF project, in a partnership including several industrial (Ascometal, Cetim, PSA, Transvalor, Atelier des Janves, Gévelot) and academic (INSA Lyon MATEIS, ENSMP-CEMEF, Arts et Métiers ParisTech LAMPA) institutions.

This paper is dedicated to the high cycle fatigue (HCF) behaviour of cast Al–Si alloys. In particular, three similar alloys with different microstructural characteristics are investigated. The result of an experimental campaign is presented, in order to characterise the fatigue behaviour, and more specifically the fatigue damage mechanisms related to the different microstructural heterogeneities (i.e. casting porosity, dendrite size, SDAS, non-metallic inclusions and silicon particles), observed under different multiaxial loading conditions: pure tension, plane bending, pure torsion and combined tension–torsion with a load ratio R=−1. It is shown that casting porosity has a very detrimental influence on the uniaxial and combined tension–torsion fatigue strengths. However, a much lower influence is observed for the torsional fatigue strength. For the porosity-free alloy, it is observed that the formation of persistent slip bands (PSB) in the aluminium matrix is the major fatigue crack initiation mechanism regardless of the loading modes, at a load ratio of R=−1. It is also shown that the aluminium matrix has a large role in the formation of PSB and that the Si particles facilitate the formation of PSB.

The stress distribution ahead of a notch is of great practical interest when undertaking fatigue and fracture analyses. In particular it is generally the first principal stress close to the notch which is desired. For a sharp notch this can be characterized by the stress field parameter KN which is referred to as the notch stress intensity factor (or N-SIF). The finite element method is a very powerful tool which is commonly used to determine KN. However, unless specialized methods are used the finite element mesh must be extremely refined in the region of the notch in order to calculate an accurate value. In practical situations, the degree of mesh refinement necessary is often not possible, due to either time or computer limitations.

Pas d'embargo connu sur Sherpa Romeo; International audience; This study aims at providing a better understanding of the effects of both microstructure and defect on the high cycle fatigue behavior of metallic alloys using finite element simulations of polycrystalline aggregates. It is well known that the microstructure strongly affects the average fatigue strength and when the cyclic stress level is close to the fatigue limit, it is often seen as the main source of the huge scatter generally observed in this fatigue regime. The presence of geometrical defects in a material can also strongly alter the fatigue behavior. Nonetheless, when the defect size is small enough, i.e. under a critical value, the fatigue strength is no more affected by the defect. The so-called Kitagawa effect can be interpreted as a competition between the crack initiation mechanisms governed either by the microstructure or by the defect. Surprisingly, only few studies have been done to date to explain the Kitagawa effect from the point of view of this competition, even though this effect has been extensively investigated in the literature. The primary focus of this paper is hence on the use of both FE simulations and explicit descriptions of the microstructure to get insight into how the competition between defect and microstructure operates in HCF. In order to account for the variability of the microstructure in the predictions of the macroscopic fatigue limits, several configurations of crystalline orientations, crystal aggregates and defects are studied. The results of each individual FE simulation are used to assess the response at the macroscopic scale thanks to a probabilistic fatigue criterion proposed by the authors in previous works. The ability of this criterion to predict the influence of defects on the average and the scatter of macroscopic fatigue limits is evaluated. In this paper, particular emphasis is also placed on the effect of different loading modes (pure tension, pure torsion and combined tension and torsion) on the experimental and predicted fatigue strength of a 316 stainless steel containing artificial defect.

This paper presents a new model that accounts, on a local scale, for the coupling between plasticity due to gliding in shear bands and damage occurring when the accumulated plastic strain has reached a threshold value. The irreversible thermodynamics with internal state variables is employed to keep a middle way between extensive description of plastic and damage flow and application of accessibility requirements. Plasticity and damage are governed by their proper complementary rules (yield functions and potentials). At the same time, a coupling occurs between the damage variable and the hardening parameters. A large experimental database relative to the fatigue behavior of a mild steel C36 submitted to different loading modes (tension, torsion, combined proportional tension and torsion) proves the efficiency of such a model. The prediction of Wöhler curves for cyclic complex stress states can be readily done, but the main feature of this approach is to ensure a clear link between mesoscopic parameters like the hardening behavior of individual grains and the subsequent local damage.

This paper aims to propose a new interpretation of several energy-based critical plane high cycle fatigue criteria. More exactly, the meaning of several global energy-based criteria is detailed from the calculation of normal and shear work on a critical plane. This study is limited to multiaxial fatigue under constant amplitude and synchronous loadings (proportional or non-proportional), with or without mean load. After a short review of some energy-based criteria using the critical plane concept or a global approach, the reasons why energy-based critical plane criteria are more and more developed in literature are summarized. It is shown that a direct link exists between critical plane energy parameters and global ones. A critical examination of the famous Findley et al. experiments is proposed and the previous link is illustrated with two mesoscopic criteria developed by Papadopoulos and the global energy-based criterion of Banvillet et al. This leads us to propose an interpretation of fatigue crack initiation from the mesoscopic scale up to the macroscopic scale either with stress and strain quantities or with strain energy parameters.

The stress gradient and the size of a component are known to influence the fatigue strength of metallic components. Indeed, in high-cycle fatigue, experiments prove that the stress distribution as well as the size of the loaded specimen can be responsible for changes in the fatigue limit (for instance, the fatigue limits in tension and bending are different, and decrease with the size of the specimen). When dealing with multiaxial load conditions, those effects still act but a relevant criterion must be used to account for the complex state of stress. The weakest-link concept together with a multiaxial endurance criterion based on a microplasticity analysis are then combined to describe the fatigue limit distribution of different metallic materials. Several load conditions are analysed: tension-compression, torsion, rotating bending and plane bending. By means of the proposed model, all the known effects on fatigue strength can be reflected. First, the endurance probability can be adequately predicted for any complex load conditions knowing some reference data from uniaxial fatigue tests. It can be linked to the probability of finding a defect with a critical size. The weakest-link theory also accounts for the decrease of multiaxial fatigue limit with the stressed volume. For the same load condition (i.e. for the same stress distribution in the volume), the probability of finding a critical defect increases with the component size and then according to the weakest-link theory the fatigue strength drops. A second model, based only on the damage developed at the surface, is also proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects such as nodular cast iron, the new surface approach distinguishes between surface and volume effects.

This issue of Fatigue and Fracture of Engineering Materials and Structures contains a collection of manuscripts presented at the Second International Symposium on Fatigue Design and Material Defects (FDMD II) held in Paris, France, on June 11 – 13, 2014 organized by the French Society for Metallurgy and Materials (SF2M) and the German Association for Materials Research and Testing (DVM).

The stress gradient effect on the fatigue limit is an important factor which has to be taken into account for an efficient transfer of fatigue data from laboratory tests to design of industrial components. A short review of some multiaxial high cycle fatigue criteria considering this effect is presented. On the basis of the two local mesoscopic approaches of Papadopoulos, two new non-local high cycle multiaxial fatigue criteria are developed. These proposals are based on the concept of volume influencing fatigue crack initiation. Their predictions are compared with experimental multiaxial fatigue data on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron). The accuracy of the two local Papadopoulos criteria and of the non-local proposals are compared and discussed, together with the physical interpretation of the threshold defining the volume influencing fatigue crack initiation.

International audience; This work investigates the effect of natural and artificial surface defects and quenching on the fatigue strength of a Boron steel (22MnB5). A vast experimental campaign has been undertaken to study the high cycle fatigue behaviour and more specifically the fatigue damage mechanisms observed in quenched and untreated materials, under different loading conditions and with differents artificial defects sizes (from 25 μm to 370 μm radius). In order to test the sheet metal in shear an original test apparatus is used. The critical defect size is determined to be 100 ± 50 μm. This critical size does not appear to depend on the loading type or the microstructure of the material (i.e. ferritic-perlitic or martensitic). However, for large defects, the quenched material is more sensitive to the defect size than the untreated material. For a defect size range of 100-300 μm the slope of the Kitagawa-Takahashi diagram is approximately −1/3 and −1/6 for the quenched and untreated materials respectively. A probabilistic approach that leads naturally to a probabilistic Kitagawa type diagram is developed. This methodology can be used to explain the relationship between the influence of the heat treatment and the defect size on the fatigue behaviour of this steel.

Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed. Financial support of this research by Arts et Métiers Paristech is gratefully acknowledged.

This study aims to analyse the influence of geometrical defects (notches and holes) on the high cycle fatigue behaviour of an electrolytic copper based on finite element simulations of 2D polycrystalline aggregates. In order to investigate the role of each source of anisotropy on the mechanical response at the grain scale, three different material constitutive models are assigned successively to the grains: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. The significant influence of the elastic anisotropy on the mechanical response of the grains is highlighted. When considering smooth microstructures, the crystal plasticity have has a slight effect in comparison with the cubic elasticity influence. However, in the case of notched microstructures, it has been shown that the influence of the plasticity is no more negligible. Finally, the predictions of three fatigue criteria are analysed. Their ability to predict the defect size effect on the fatigue strength is evaluated thanks to a comparison with experimental data from the literature.; International audience; This study aims to analyse the influence of geometrical defects (notches and holes) on the high cycle fatigue behaviour of an electrolytic copper based on finite element simulations of 2D polycrystalline aggregates. In order to investigate the role of each source of anisotropy on the mechanical response at the grain scale, three different material constitutive models are assigned successively to the grains: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. The significant influence of the elastic anisotropy on the mechanical response of the grains is highlighted. When considering smooth microstructures, the crystal plasticity have has a slight effect in comparison with the cubic elasticity influence. However, in the case of notched microstructures, it has been shown that the influence of the plasticity is no more negligible. Finally, the predictions of three fatigue criteria are analysed. Their ability to predict the defect size effect on the fatigue strength is evaluated thanks to a comparison with experimental data from the literature.

This paper presents an easy to handle but efficient fatigue life prediction method based on a plasticity analysis carried out at the scale of the grains, i.e. the mesoscopic scale. The different steps of the model are described in the case of in-phase as well as out-of-phase bending-torsion load conditions. One striking feature of this method is that the definition of the critical material plane and the estimation of the number of cycles to initiation are made by means of analytical expressions that are functions of the loading parameters such as amplitudes, means and phase angles. The identification of the model parameters is readily carried out by means of one SN curve and two fatigue limits. This model is able to reflect the influence of the phase shift on damage accumulation with the introduction of no adjustable parameters. Furthermore, the comparison between the predictions and in-phase and out-of-phase fatigue data found in the literature leads to very good correlation.

In this paper, a new life prediction method for high cycle multiaxial fatigue of metallic materials is presented. It is based on a local approach introduced by Dang Van and developed by Papadopoulos, where accumulated plastic strain due to external loading is estimated at a scale of the order of a few grains. Its evaluation requires the use of a critical plane type fatigue criterion. As soon as the accumulated plastic mesostrain, considered as the damage variable, reaches a critical value, a crack is considered to be initiated. The complex and combined cases of loading (multiaxial and variable amplitude loading) can be analysed with this new method. In particular, attention is given to a description of the damaging effect of the loading path shape on fatigue strength. The application of hardening plasticity laws at the local scale allows one to estimate and sum the damage caused by elementary loading events like transitions.

The aim of this paper is to present a high cycle multiaxial fatigue life prediction method for metallic materials based on Papadopoulos' previous works and limited to constant amplitude loading. The initiation process of a crack is treated as a mesoscopic phenomenon taking place on a scale of the order of a grain or a few grains. The damage variable chosen is the accumulated plastic strain at this mesoscopic scale. Its estimation requires a macro-meso passage and the location of the plane subjected to maximum damage. Initiation is achieved as soon as a critical value of the accumulated plastic mesostrain is reached in these grains, so-orientated that their easy glide directions coincide with a particular direction of the critical plane. The detrimental effect of out-of-phase loading on damage accumulation is taken into account through a newly defined coefficient estimated from mechanical loading parameters; no adjustable parameter is required. A good agreement has been found between the predicted and experimental results for in-phase and out-of-phase sinusoidal constant amplitude loadings by examining a large amount of experimental data.

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 107 cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.; International audience; In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 107 cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.

This paper presents the results obtained with a new ball burnishing tool developed for the mechanical treatment of large flat surfaces. Several parameters can affect the mechanical behavior and fatigue of workpiece. Our study focused on the effect of the burnishing force on the surface quality and on the service properties (mechanical behavior, fatigue) of AISI 1010 steel hot-rolled plates. Experimental results assert that burnishing force not exceeding 300 N causes an increase in the ductility. In addition, results indicated that the effect of the burnishing force on the residual surface stress was greater in the direction of advance than in the cross-feed direction. Furthermore, the flat burnishing surfaces did not improve the fatigue strength of AISI 1010 steel flat specimens.

During forging and machining manufacturing processes, the material is subject to large strains at high strain rates which provoke local heating and microstructural changes. Modelling of these phenomena requires precise knowledge of the stress–strain constitutive equations for a large range of strains, strain rates and temperatures. An experimental study of the rheology of both hyper- and hypo-eutectoid steels (with different microstructures) over a temperature range from 20 °C to 1000 °C and with strain rates from 10 − 2 to 10 5 s − 1 has been undertaken. These tests were performed in compression on cylindrical specimens and in shear using hat-shaped specimens. Both a GLEEBLE 3500 thermomechanical testing machine and a Split-Hopkinson Pressure Bar apparatus were used. From these tests, three deformation domains have been identified as a function of the material behaviour and of the changes in the deformed microstructure. Each domain was characterized by its behaviour, including the competition between hardening and softening, strain rate sensitivity on the flow stress and the softening phenomenon (i.e. recrystallisation or recovery, etc.). Finally, based on thermodynamical considerations, the conditions of thermoplastic instability (i.e. shear bands, twinning, heterogeneities, etc.) and microstructural changes are highlighted using process maps of the dissipated power repartition.

Lien vers la version éditeur: http://www.sciencedirect.com/science/article/pii/S0142112312002472; International audience; This article is dedicated to the high cycle fatigue behaviour of cast hypo-eutectic Al-Si alloys and in particular the AlSi7Cu05Mg03 alloy. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms operating in this alloy, subject to complex loading conditions, it was shown that two different coexisting fatigue damage mechanisms occur in this materials, depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Si particles, Fe-rich intermetallic phases, DAS of the Al-matrix, etc.). In order to take into account both of these damage mechanisms, a probabilistic approach using the weakest link concept is introduced to model the competition between the two mechanisms. This approach leads naturally to a probabilistic Kitagawa type diagram, which explains the relationship between the fatigue behaviour of the material and the different casting processes or post-treatments (e.g. gravity casting and HIP). It is shown that the sensitivity to the different loading modes (i.e. uniaxial with and without mean stress, torsion and equibiaxial tension) depends on the microstructural heterogeneities responsible for crack initiation. For a porosity-free alloy, the predictions are very good for combined tension-torsion loading modes. When pores are present and control the fatigue strength, the predictions are very satisfactory for the uniaxial loads with different R-ratios and slightly conservative for multiaxial loads (i.e. torsion and equibiaxial tension). Never-the-less, they are much better than the predictions of the Dang Van criterion [1].

Lien vers la version éditeur: http://www.sciencedirect.com/science/article/pii/S0142112312002356; International audience; This article is dedicated to the high cycle fatigue behaviour of cast hypo-eutectic Al-Si alloys. In particular, the AlSi7Cu05Mg03 alloy is investigated. It presents the results of a vast experimental campaign undertaken to investigate the fatigue behaviour, and more specifically the fatigue damage mechanisms observed under complex loading conditions: plane bending with different load ratios, fully reversed torsion and equibiaxial bending with a load ratio of R = 0.1. A specific test set-up has been designed to create an equibiaxial stress state using disk shaped specimens. A tomographic analysis is also presented with the aim of characterising the micro-shrinkage pore population of the material. It is shown that two distinct and coexisting fatigue damage mechanisms occur in this material, depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Silicon particles in the eutectic zones, Fe-rich intermetallic phases, etc.). Furthermore, it is concluded that the effect of an equibiaxial tensile stress state is not detrimental in terms of high cycle fatigue. It is also shown that the Dang Van criterion is not able to simultaneously predict the multiaxial effect (i.e. torsion and equibiaxial tension) and the mean stress effect for this material.

The objective of this work is to propose an anisotropic fatigue criterion for the sizing of industrial forged components. The results from different experimental campaigns using three different rolled steels are first presented. The effect of inclusions and the microstructure on the fatigue behaviour are investigated. For the two ferrite-pearlitic steels tested, the presence of a microstructure consisting of elongated grains has no observable effects on the fatigue behaviour. For two of the three steels studied the presence of non-metallic inclusions, elongated in the rolling direction, form the origin of the anisotropic fatigue behaviour. The proposed probabilistic model is based on the competition between two possible fatigue crack initiation mechanisms. The anisotropic character of the fatigue resistance of forged components is taken into account by the definition of the geometry and the orientation of the non-metallic inclusion. This criterion results in the establishment of a probabilistic Kitagawa type diagram. This work was undertaken with the framework of the Optiforge project which was supported by the French “Agence National de la Recherche”. These results are the product of cooperation between industry partners (Ascoforge, Ascometal, Cetim, PSA, Setforge and Transvalor) and academic partners (INSA Lyon-MATEIS, ENSMP-CEMEF, Arts et Métiers PARISTECH Angers-LAMPA).